Batman is called Batman because he looks like a bat and flies like them. Same with Spider-Man and Superman carrying a S mark of on his chest. But why is Deadpool named Deadpool? I mean why Deadpool and what makes him Deadpool? Is this explained anywhere in the movie or is this solely a remnant of the comics?
At first, Deadpool was just a generic mercenary bad guy, during the XTREME era of comics, the 90s. The name was a typical extreme villain name. It was also a barely hidden play on the DC character Deathstroke, Slade Wilson, who Deadpool was basically a copy of at first.
Then after his popularity went up, and Deadpool became a starring character, they gave him a canon back story.
Deadpool got his name from a betting pool at the Hospice, where "failed" members of Department K/Canadian branch of the Weapons X program were sent for treatment. But the Hospice was being used by Dr. Killebrew as a source of human lab rats for experiments, not part of the official Weapon X program. Ajax helped Dr. Killebrew.
The "patients", the other inmates, not the guards, were betting on when test subjects would die from the experiments. A "When will they be Dead" pool. Worm, Deadpool's friend in the Hospice, handles the pool:
Wade survived much longer than anyone expected, courtesy of his willpower and the mutant healing factor embedded in him earlier. It didn't start working until Ajax tried to kill him, ripping Wade's heart out. He regenerated, attempted to kill Ajax, breaking out of the Hospice, winning the dead pool, and the name stuck.
Deadpool in the movie is named Deadpool after the fact. It's much less relevant to his character in the movies than it was in the comics. The bar that Wade goes to is "Sister Margaret’s Home for Wayward Girls.", officially known as the Hell House in the comics. The betting pool in the bar is for regular mercenaries, hired guns, hitmen, or any degenerate going there. It is a dead pool, seeing when these guys (filled with a bunch of random references) will kick the bucket. It has no connection to the Hospice, or Dr. Killebrew. Ajax is not known as the Attending. Worm is not the one that introduces Wade to the Dead Pool. Etc. Wade was on the dead pool long before his cancer or failed Weapon X procedures. After he escapes Ajax the first time, he meets Weasel and they brainstorm names in-between insults. Wade ends up taking the name Deadpool from the bar's betting pool, just riffing with Weasel.
He literally takes it 2 seconds after he saw it on the wall, instead of feeling attached to it due to months of torture by Killebrew at the Hospice. One of the less than stellar changes they made to his origin story. Of course, the real reason the movie Deadpool is named Deadpool is because he's a comic character and they can't change the name.
In the Deadpool and Death Annual 1999 we learn the origin of Deadpool's name; simply put, when he was being experimented on (as part of the programme which ultimately led to his powers) the guards had a dead pool where they would gamble on which subject would die next. He took his name from this.
Out of universe, ComicVine indicates that the name (and concept) were chosen as an homage to the 5th Dirty Harry movie. Although they're usually very accurate about these things, I can't find any quotes to back this up.